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A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by: E(t) = E0e-i[omega]0t - t/2[tao], where E0 is a compex constant, while [omega]0 and [tao] are real constants. a) Determine the detected time-dependent intensity I(t) = |E(t)|2. b) Determine the frequency resolved intensity I([omega]) = |E([omega])|2, where E([omega]) = The integral from 0 to infinity of E(t)*ei[omega]t dt.

A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by: E(t) = E0e-i[omega]0t - t/2[tao], where E0 is a compex constant, while [omega]0 and [tao] are real constants. a) Determine the detected time-dependent intensity I(t) = |E(t)|2. b) Determine the frequency resolved intensity I([omega]) = |E([omega])|2, where E([omega]) = The integral from 0 to infinity of E(t)*ei[omega]t dt.

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A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by:

E(t) = E0e-i[omega]0t - t/2[tao], where E0 is a compex constant, while [omega]0 and [tao] are real constants.

a) Determine the detected time-dependent intensity I(t) = |E(t)|2.

b) Determine the frequency resolved intensity I([omega]) = |E([omega])|2, where E([omega]) = The integral from 0 to infinity of E(t)*ei[omega]t dt.

c) Determine the frequency [omega]max where I([omega]) attains its maximum, as well as the full width at half maximum [delta omega], defined by I([omega]max +/_ [delta omega]/2) = (1/2)I([omega]max).

d) Sketch the time-dependent and frequency-resolved intensities I(t) and I([omega]).

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A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by E(t) = Eo exp(-iwot – t/27), where Eo is a complex constant, while wo and T are real constants. (a) Determine the detected time-dependent intensity I(t) = |E(t)|². (b) Determine the frequency-resolved intensity I(w) = |E(w)]², where E(w) = | E(t) exp(iwt) dt. (c) Determine the frequency wmax where I(w) attains its maximum, as well as the full width at half maximum Aw, defined by I(wmax ±Aw/2) = (1/2)I(wmax). (d) Sketch the time-dependent and frequency-resolved intensities I (t) and I(w).
Transcribed Image Text:A cloud of atoms is excited by a laser pulse and then emits electromagnetic radiation, which is detected by a spectrometer. At the detector, the amplitude of the field is given by E(t) = Eo exp(-iwot – t/27), where Eo is a complex constant, while wo and T are real constants. (a) Determine the detected time-dependent intensity I(t) = |E(t)|². (b) Determine the frequency-resolved intensity I(w) = |E(w)]², where E(w) = | E(t) exp(iwt) dt. (c) Determine the frequency wmax where I(w) attains its maximum, as well as the full width at half maximum Aw, defined by I(wmax ±Aw/2) = (1/2)I(wmax). (d) Sketch the time-dependent and frequency-resolved intensities I (t) and I(w).
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